Evaluation of robust scale estimators for modified Weibull process capability indices and their bootstrap confidence intervals

Abstract

Process capability index (PCI) evaluations in reliability analysis require modified production range estimators. Reliability datasets are often attempted to be modelled using the Weibull distribution. Adopting the original PCI model which was first proposed by Juran simplifies the overall effort while furnishing useful results. This is because of isolating the problem solely to the scale estimators. In turn, this makes the results more widely relevant than focusing on particular specification ranges and predefined PCI performance levels. To assess the non-normal performance of a PCI under a Weibull reference law, it is imperative to understand the behavior and limitations of key robust scale estimators that comprise a PCI. In this study, we consider the robust estimators: (1) the interquartile range (IQR), (2) the median absolute deviation (MAD) and (3) the Qn estimator. Four typical Weibull distributions have been selected with distinctly different probability density characteristics to probe the tendencies of the three robust estimators. Jackknife standard errors and biases are estimated. Four bootstrap resampling methods are used to obtain 95% confidence intervals for the three robust estimators. Three typical sampling sizes are investigated that may have practical meaning in real operations. Furthermore, a pragmatic paradigm from a published reliability study concerning the breakdown performance of an insulating fluid is evaluated from a robust scale perspective. We discuss the advantages and disadvantages of the three robust scale estimators as well as discrepancies with past research.